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# Prove that for the system dx dt = F( x, y), dy dt = G( x, y) there is at most one ISBN: 9781119256007 392

## Solution for problem 22 Chapter 9.2

Elementary Differential Equations and Boundary Value Problems | 11th Edition

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Problem 22

Prove that for the system dx dt = F( x, y), dy dt = G( x, y) there is at most one trajectory passing through a given point ( x0, y0). Hint: Let C0 be the trajectory generated by the solution x = 0(t), y = 0(t), with 0(t0) = x0, 0(t0) = y0, and let C1 be the trajectory generated by the solution x = 1(t), y = 1(t), with 1(t1) = x0, 1(t1) = y0. Use the fact that the system is autonomous, and also the existence and uniqueness theorem, to show that C0 and C1 are the same. 2

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##### ISBN: 9781119256007

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